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Full text of "Isometric and Trimetric Drawing"

ISOMETRIC 



AND 



TRIMETRIC 
DRAWING 




C. B. LOWE 






ISOMETRIC 

AND 
TRIMETRIC 



|« 



PRESTON POLYTECHNIC 
LIBRARY & LEARNING RESOURCES SERVICE 

This book must be returned on or before the date last stamped 




PLEASE RETURN TO CAMPUS INDICATED 

Lancaster Annexe Tel. 88121 

Poulton Campus Tel. 884651 

Preston Campus Tel. 58692 
30 



\ZL 







C. B. LOWE 



A HEYWOOD BOOK 
LONDON 1963 

TEMPLE PRESS BOOKS LTD 



C. B. LOWE 1963 



HARRIS, 




Filmset and reproduced by Photoprint Plates Ltd., Basildon, Essex 

and 
Printed in England by Perivan (Litho) Ltd., Southend-on-Sea 



Whilst it has become increasingly recognized that Isometric views 
are almost essential for explanatory hand-books of various mechanisms, 
sometimes by way of ghost drawings, and in other cases by exploded 
views showing the component parts, it does not seem to have been 
generally recognized that the advantages and clarity of this form of 
portrayal can be applied in an equal degree to actual working drawings. 

One of the reasons may be that heretofore there has not been 
available a simple work to form a basis for instruction in its practical 
application. I consider that Isometric and Trimetric Drawing does meet 
this requirement. 

In my experience on automobile and aircraft armament design and 
construction, too few of the draughtsmen I have known have been 
able to make pictorial engineering drawings, due either to their 
non-appreciation of its benefits, or their lack of the constant practice 
by which it becomes a quick and easy medium of expression. 

Those who use it freely have, in my opinion, a much more facile 
designing ability than those unversed in its art. 

This book is written in simple language and includes small but 
important points which, though valuable, I have not previously seen 
brought forward. 

Mr C. B. Lowe has long been an advocate of pictorial engineering 
drawing and I am very glad to see that in this hand-book he has put 
his wide knowledge of the subject within reach of our coming 
draughtsmen and designers. 

A. Fraser-Nash 
2- 1 0-62 



Orthographic, or flat, drawing employing three or more views will 
always be the main method used when recording or setting out 
dimensioned shapes. These are drawn using either first or third 
angle projection. There are many occasions, however, when the 
addition of a three-dimensional view would be most helpful in order 
to clarify some particularly obscure feature. 

Sometimes even engineers with long experience are puzzled 
when studying ordinary flat drawings of complicated parts, which 
although correctly drawn, may have some detail which is not im- 
mediately understood. It is in such cases that the inclusion of additional 
pictorial views has great value, permitting instant recognition of 
complicated shapes and detail which might otherwise be obscure. 

Pictorial drawing may be carried out in three main ways: 

Isometric, The simplest form. 

Trimetric, More difficult but sometimes necessary. 

Perspective, Essential for artistic representation. 

Of these, isometric is the most favoured because of its relative 
simplicity. This is brought about by the fact that its three planes are 
equally tilted to the eye of the beholder and so have equality of 
measure along the edge lines. It must be admitted, however, that this 
equal tilting can bring disadvantages in some rare cases; for instance 
certain simple forms can appear to turn themselves inside-out, but 
this is an optical illusion which ceases as the drawing grows with 
added detail. 



The only other slight disadvantage which might occur is the 
coincidence of some lines being in the direct sight path of others. 
When this is likely to occur, the draughtsman would be wise to use a 
trimetric attitude with the most direct plane (the fullest plane) 
showing the feature or features which require particular emphasis. 

Both isometric and trimetric drawing are geometrically pure 
forms of drawing, being projections from orthographic views. There 
is no need for guesswork. Perspective vanishing does not occur in 
isometric or trimetric drawing; both, however, may be regarded as 
perspective at an infinite distance. To some extent the lack of vanish- 
ing is evident; it depends very much on the aspect ratio of the subject 
depicted. In compact subjects it is barely noticeable, particularly if 
they contain a lot of detail. 

In any case we must keep in mind the fact that we are not trying 
to produce an artistic creation but a clear and easily understood 
mechanical document which is obvious in its meaning to all who study 
it. 

All draughtsmen should be able to draw in isometric and in 
trimetric. They are not difficult once the main rules are mastered. 

Perspective drawing, a most absorbing subject, is not taught in 
this book. It requires constant practice and is generally left to spe- 
cialists. 



8 



9djome&uc P>vojectixM 

HAVING EQUALITY OF MEASURE— ISOS equal. METRON measure 

Isometric Projection is a method of drawing solid objects using the 
same scale of linear measurement on each of the three planes. 

This is done by picturing the object cornerwise and at such a 
downward angle that each plane is equally inclined to the view, as 
in the figure below. 

Because each plane is equally inclined, all edges are proportion- 
ately reduced in apparent length, being foreshortened to a known 
ratio. It is necessary therefore to use a smaller scale when producing 
isometric drawings. 

The reason for this reduced scale, and how it is determined, 
must be clearly understood by the draughtsman if he is to be con- 
fident of every line of his drawing. 

To this end, a simple exercise is given in the diagrams overleaf. 
Using everyday articles as models such as a matchbox and a cube of 
sugar, arrange them so that when viewed from above they appear 
as set out in the top figure overleaf. 




Standing square to the desk or 
board on which they are placed, look 
downward and you see the plan view, 
Figure I . 

Moving backwards in a straight 
line, but still keeping square to the 
desk, you will see an ever-changing 
aspect, and the front corner angles 
of the box and cube will appear 
gradually to change from 90° to some 
increased angle according to the angle 
of view, as in Figures 2 and 3. 

If your angle of view alters so 
much that your sight line is 90° from 
its original position then natucally 
the angles will have opened out so 
that they now form a straight hori- 
zontal line, the whole forming a cor- 
ner elevation, Figure 4. 

The isometric view lies between 
the two extremes and it will be 
noted how the dotted lines repre- 
senting the invisible edges of the 
cube meet at the same point as the 
top front corner of the cube. Thus 
the nine lines forming the visible 
edges are all of the same length. 
Only in an isometric cube does this 
occur. 

By comparing the length of the 
box taken from the plan with the 
lengths in other views, you will see 
the variation in amounts of fore- 
shortening. 




Figure 



Edge of desk 



or board 



Isometric 
view 




Figure 2 



Figure 3 



Corner 
elevation 



Figure 4 



10 



^Ue OiXHtoet/iic Scale 

Having seen the necessity of a reduced scale, we now learn how it is 
determined. It is a precise measurement for a given degree of fore- 
shortening and its ratio to flat measure should be fully understood. 
If we draw an inch cube isometrically but neglect to use the 
isometric scale it will look like Figure 5, i.e. too large. 




Figure 5 



Compare the incorrectly scaled 
cube above with the cube drawn 
to correct scale, right. (Figure 6.) 
It will be seen, therefore, 
that the reason for using a speci- 
ally reduced scale is because we 
are drawing lengths which are 
at an angle to our vision. 



Edges measured 
with ordinary inch 



One i 
isom^f 



One inch 
isometric 




Isometric view 



Orthographic 
Plan view 



One m,ch 
ordinar 



Figure 6 



There are certain parts of isometric or trimetric which retain 
ordinary scale. A sphere for example can only appear at its true 
diameter no matter from what angle it is being regarded. It can never 
be anything other than its true diameter. For the same reason a 



II 



circular shaft or cylinder always shows its full diameter, as do circular 
holes, their full diameter being expressed as the major axis of an ellipse. 

Figure 7 



In Figure7a l^-in. cube 
is shown with a circular 
feature on each of its planes. 

Note that all repre- 
sentations of diameter, ex- 
pressed by ellipses, have 
full scale on their major axes. 




Two Methods of making an Isometric Scale: 



TOP PLANE 

I* dia. X I* lonq 
cylinder 



RIGHT HAND PLANE 

/& dia. cylinder 
lonq 



LEFT HAND PLANE 



\/A di 



a. recess 



Figure 8 



/a- deep 




Scale need, not start 
at intersection of angles 



12 



There may be a little confusion in connection with the isometric 
sight angle, which may be taken as 35°, and the 30° angle at which 
normal isometric lines are drawn. 

Referring back to the cube of sugar in Figure 2 you will remember 
that at the isometric angle of view, the top front corner of the cube 
(solid lines) meets the bottom rear corner (dotted lines). Thus, nine 
solid lines depict the visible cube edges and three dotted lines indicate 
the hidden edges. These twelve lines are all of the same length, in fact 
the isometric cube is constructed from six equilateral triangles fitting 
together to form a hexagon, with two of its sides vertical, for the 
outside shape. From this you will see how the 30° angle comes to be 
used for normal isometric lines. It will also correct the mistaken 
belief held by some, that the 30° angle has been chosen as convenient 
because set squares are made to that angle. 

The 30° angle at which isometric lines are drawn, must not be 
confused with the sight angle 
(the angle at which you are 
looking downwards). The sight 
angle, which from now on will 
be shown by the symbol > is 
decided by the fact that we are 
looking down on the cube placed 
cornerwise so that our sight line 
passes through its furthermost 
corners. How we arrive at this is 
shown in Figure 10. 




Figure IO 



13 



When a circle is tilted to the eye it becomes an ellipse. 









Isometric ellipse 



Figure 



Equilateral 
triangle 




Ellipses around a given axial centre line all have the same major/minor 
proportion. This applies to isometric ellipses or others. 



Focal points 





Focal points 



A small nick in pencil lead 
prevents overriding thread 



Figure I 2 



Hold ends of thread 
firmly with finger 




14 



*lUa ZUifAe. 



The ellipse is the most beautiful of all geometric shapes and the care 
taken in drawing it is amply repaid. Approximate curves made by a 
combination of radii should be avoided as they are usually distorted 
and most displeasing. A freehand ellipse is better than one made by 
radii. Correct major to minor proportions are necessary and in the 
case of isometric ellipses are easily decided, as shown in Figure 1 1. 

The most practical way of striking elliptical curves is by using 
cotton or nylon thread as shown in Figure 12 (opposite). The radius of 
the arc for obtaining the focal points is equal to half the major axis 
for an ellipse of any size or proportion. 

Elliptical masks are a boon to the draughtsman enabling him to 
draw ellipses crisply and quickly, but if these aids are not available 
ready-made, they can be made from thin cardboard or stiff paper. 
When making them, it is helpful to add two cross lines at 30° to the 
major axis in addition to the major and minor axis lines for they 
indicate at which point to stop the pencil when drawing arcs such as 
those for the corner radii in Figure 12 (below). 



true ellipse 





Figure 12 



Approximate ellipse 
formed by radii 

15 



AwcjmIgSi SuAfecti 



Before starting a three-dimensional drawing, be it isometric or tri- 
metric, it is necessary to have before you an orthographic drawing of 
the subject to be illustrated. 

When setting out angles on any of the three planes it is not pos- 
sible to use an ordinary protractor because the angles need to be 
converted; angles, like lengths, become foreshortened. Each angular 
line on any plane must therefore be subject to the scale of lengths used 
on that particular plane. 

To determine an angle, we know that a line rises so much in a 
distance of so much. In flat drawing these distances or lengths are at 
right angles to each other. They are not so in three-dimensional 
drawing, as can be seen below, Figure 13 (right). 



^^--20° 




X 


t 

L Ordinary 




sc a le 





(Ll 

D 
U 



2r 

o 
c 

o 



Figure 




Converted to 
isometric scale 



It is helpful to have the symbol cube before you, for it avoids 
confusion and shows from which datum the angle is to be measured. 
When setting out angles on trimetric planes, H and L are converted to 
the scale used for the particular direction concerned. 



16 



The ellipse of correct proportion and at its correct orientation for 
its given plane provides an 'on the spot' means of measurement 
for foreshortened lengths in any direction on that plane if the measure- 
ments are made on lines from the ellipse centre or parallel with 
them. (Figure 14.) This rule applies to all planes, isometric or other- 
wise. It is essential to use an ellipse of 
the correct proportion for the plane 
in question. 

From these varying lengths it is 
now a simple matter to find the pro- 
portions of ellipses which represent 
circles around the radial lines, which 
now become axial centre lines. 

A study of the drawing on page 19 will show you the following facts: 

All cylinders can be measured across their parallel lines. 

All major axes are at right angles to the cylinder centre lines. 

Scales used for radial lengths vary with their angular attitude. 

The proportions of cylinder lengths to minor axes are in inverse 

ratio. 



Fiqure I 4 

The length of any 
line across this 
ellipse, if drawn 
through its centre, 
represents one inch in the direc- 
tion of that line 

See also Fiqure 26 




Minor axis for 
V/\ maj 



J 



Siqht anqle level 
no minor axis 



Fiqure 15 



By comparing a 
-v foreshortened length 
with its ordinary (flat) 
length as in Figure 15, 
we determine the sight 
angle, shown thus: > 
and using this we ob- 
tain the minor axis for 

Lenqth of arcs are 

foreshortened lenqths a known major axis. 




17 




18 



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19 



THREE DIMENSIONAL DRAWING WITH UNEQUAL PLANES 

Trimetric drawing is a branch of descriptive geometry by which 
objects are viewed at different angles from those used in isometric 
projection. It is of course possible to depict an object at any angle to 
the eye, the extreme case being when one or even two of the co- 
ordinate planes are so foreshortened that they almost fade out of the 
picture, as in Figure 19. 




Fiqure I 8 



Figure 19 



No purpose is served by drawing views with excessive foreshorten- 
ing unless special requirements demand that particular aspect. Some of 
the most useful aspects are those in which one plane of the figure is 
parallel to one of the isometric^planes. This also permits the use of 
isometric ellipse masks and scales, should you possess them. 

It has been shown that objects resting at an angle on the isometric 
plane are not difficult to draw, and in this manner, we are introduced 
to Trimetric aspects. 



20 



Figure 17 on page 19 shows a ring of cylinders set out on the top 
isometric plane, (it could be on either of the other planes); each 
cylinder has a cube at its outer end. Each and every cube on the 
perimeter retains the isometric scale for the vertical lines as it is 
resting on an isometric plane. 

In this view the cube is shown thirty-six times, i.e. spaced 10 
isometric degrees apart, and for the purpose of analysis, this number 
may be divided by four because each aspect is repeated four times, as 
it is in the orthographic plan view. 

Examination will show that cubes 90 isometric degrees apart have 
the same aspect exactly as have the orthographic squares in Figure 16. 
We therefore have a choice of eight different aspects which are 
trimetric in addition to the isometric cubes, which are of course 
repeated four times. 

Aspect B is ideal for trimetric views because it strikes a good 
balance without too much foreshortening or being too near to the 
isometric aspect. 

Trimetric is of course more 
difficult to draw than isometric be- 
cause it requires three different 
scales, and uses ellipses of three 
different major/minor proportions, 
but it gives a wider scope for expres- 
sion by providing a choice of six 
viewing aspects using the same scales 
and ellipses. The method of setting 
out a trimetric cube is shown on page 
23. Such a cube provides you with 
Aspect B the angles and foreshortened scales. 



Figure 20 




21 



Six aspects of a I -inch cube using the same three scales and the same 

ellipses. 

In addition six upward views can be made. 




Figure 21 



Isometric 
top plane 





Figure 22 



Isometric 
inward plane 





Figure 2 3 



Isometric 
outward plane 




22 



SettUuf out a ^^Umet/Uc Cube 



To draw a Trimetric cube with its top 
plane at the Isometric angle of sight: Draw 
a plan of the top plane rotated to the atti- 
tude required. Surround it with an em- 
bracing square, drawn with a 45° set square, 
as shown by fine lines in Figure 24. Project 
the corners of the embracing square down- 
wards and set out its isometric translation. 
This diamond shaped form is drawn with a 
30° set square, and is therefore a normal 
top isometric plane. The corners of the 
inner square projected down to the dia- 
mond will give the four points from which 
the trimetric top plane can be drawn. The 
vertical edges of the trimetric cube are 

drawn to isometric scale 
so that the trimetric 
cube may be completed. 




Cube turned 
25° 




LC 



Figure 

Another method is shown in Figure 25 above. 
It is a good plan to draw a six-inch cube using this 
method. 

By dividing one of each of the edge lines into 
six equal parts you have the three scales needed 
for this aspect. 

23 



NOTE THAT THE 
SPINDLE <fcs ARE 
EACH PARALLEL TO 
EDGE LINES OF THE 
CUBE AND THAT 
MAJOR AXES OF ALL 
ELLIPSES ARE AT 
RIGHT-ANGLES TO 
AXIAL G_s. 



A 2-in. cube with three ^-in. diameter spindles 
projecting 2 in. from faces (aspect B). Each spindle 
has eight ^-in. diameter cylinders I in. long radiat- 
ing from it. These are spaced 45° apart. The scale 
length of the cylinders on each plane can be obtained 

c v „rr, n \ a ■ Tk.c i a „ n fk from the spindle ellipse 

example . I his length ~ ~ 

- D x 2 /-">v on its own plane. 



Example : 
This length 

= Ax2 




Fiqure 2 6 

Drawn at Trimetric 
aspect B 



Example : This lenqth - B x 2 



24 



Idi&lfuJL fyacti about tke ZlUpAje 

SHORT CUTS TO ACCURACY 
Three methods of correlation of ellipse proportion and scale of axial 
centre line, Figures 27, 28, 29 and 30. This is applicable to ellipses of 
any proportion. 

Figure 2 7 ^~^\ \ Figure 28 

'"Minor axis 
for 2 inch maj 



2 inch dia. cylinder 



2 inches long. 




Scale length 
of axial (£ 




o 



X 

o 



^ 



X 

< 



^T 



cr 

c 

_4> 

o 

u 

CO 



The two dots • 
are also the foci 
of the ellipse. 




Figure 30 



Half minor 
axis. 



Figure 29 It should be noted that the measurements 

obtained when using the method shown in Figure 28 
are inversive i.e. by feeding in one known factor, be it axial scale, sight 
angle or minor axis, two factors are obtained. 



25 




l>2 



The isometric ellipse. /8 major. 
is used for proportioning all the 
slots as shown. 



-^Dia. circle 



Six slots 4 wide 
equally spaced 



Figure 31 




Isometric 




o 

Drawn at 25 angle 



Any circle on the flat view which can be used 

for projection to other locations on its own 

plane can also be put to the same use when translated to its elliptical 

form on its tilted plane. 

Fiaure 3 2 




The five rings are all l^-in. outside diameter, I in. inside diameter, 
and £ in. thick. Although they have been tilted haphazardly, it was a 
simple matter to determine their foreshortened thickness. 



26 



External and internal radii are difficult to indicate because their 
merging zones are nebulous. It may, however, be considered draughts- 
man's licence to indicate them in the manner shown below, the sole 
criterion being usefulness in suggesting what is otherwise difficult to 
portray without resorting to shading. 

Fillets on castings are best depicted as shown. The intensity of 
such lines must be left to the imagination of individual draughtsmen, 
but generally it is better to make them fade out rather than to end 
them abruptly. 





Figure 33 




27 



Jiehcal BftMwfA 



The drawing of helical springs on any three-dimensional drawing 
appears at first glance to be a formidable task but if tackled in the right 
way does not present great difficulty. 

As the shape of a helical spring is repetitive along its length, 
great economy of drawing time can be brought about by the use of a 
stencil mask. This can be made from good quality thin cardboard or 
from thin transparent plastic sheet. 

Only one turn of the spring need be cut in the stencil mask (see 
Figure 37) as it can be moved along the edge of the set-square in such 
a manner as to produce the outline of a spring with as many turns or 
coils as are required. 

The first necessity is to draw the centre-line of the wire as it 
winds around the axis of the spring. 

Let us take for example a compression spring with the following 
dimensions: pitch diameter 1^ in. — pitch of helix | in. — Wire diameter 



re in- 



Set out the pitch diameter (which is of course in full scale) about 
the axis of the spring. If it is to be drawn in isometric set out its helical 
pitch in isometric scale as shown below, and divide it into four equal 

parts which will give five lines identified 
as shown. On each of these five lines 
draw an isometric ellipse — l^-in. major. 

A 



Pitch dm. 





Fiqure 34 



28 



Consider that the major and minor axes are identified as shown 
opposite, Figure 34 right. 

The next stage is to mark a point on each of the five ellipses 
starting at the top A and progressing downwards one line at a time, 
the points being a quarter of the helical pitch and a quarter of a turn of 
the diameter apart. Thus l-A, 2-B, 3-C, 4-D, and finally 5-A. 

Two points l-A and 5-A are therefore one helical pitch apart, 
and the five dots are points on the helix which is yet to be drawn. 

With practice it is possible to slide the elliptical mask downwards 
at a steady speed and at the same time move a pencil point around the 
ellipse so as to synchronize each quarter of a turn with one quarter 





Figure 1 3 6 



pitch movement, thus drawing a continuous 
helical curve for one complete coil. This merely 
represents the 'back-bone' of the spring wire, so 
it is necessary to put the 'meat on the bone' by a 
number of circles measuring the full scale dia- 
meter of the spring wire, see Figure 36. 

Think of them as spherical beads. A curve 




29 



touching their diameters gives a true silhouette outline of the spring 

coils. 

Thin wire springs may be represented by a single thick helical line 
drawn with the aid of a simple mask or directly on to the drawing using 
the slowly sliding ellipse mask. See page 37 for an example. 

SQUARE SECTION SPRINGS 
The outline curves of these springs (both inside and outside) are 
helices of the same pitch, but naturally of different diameters. These 
are most conveniently drawn with a mask as shown in Figure 38, using 

two separate openings so that by super- 
imposing the two curves upon each other the 
final outline is obtained as in Figure 39. 




Fiqure 3 8 




Figure 39 



The square section spring is viewed at a 20° angle therefore a 20 c 
ellipse mask was used for setting out the helices. 



30 



Plan 



Isometric 
angle 



// 



20 angle 



ftictosiicdLf, 

Hexagon nuts are best depicted at the 
aspect shown i.e. with three flats showing. 

Here again, the ellipse (at its correct 
tilt) is of great use for determining the 
angles of the sloping side faces. 

In the bottom view the method of 
deciding the base angles is shown with 
general construction lines. 

The thickness of the nut is of course 
measured in the appropriate scale for the 
aspect used. 



A Actual thickness of nut 

S Scale 




Figure 40 



31 



*fke Pwjeatixm o^ in/ieKjddci/i £Uxzp&i 




Figure 4 




o I 



Trimerric aspect B 



Objects of irregular shape may be drawn with a crate of structure 

lines as shown above, Figure 41. 

The shape to be translated (the flat view) is covered by a grid of 
lines equally spaced in both directions. This grid is then drawn at the 
aspect required using the appropriate scales for height, width and 
thickness used for that aspect. 

To avoid confusion, number the grid lines in both directions. It 
is a simple matter to transpose points from the flat grid to the pictorial 
grid and complete the picture with the aid of French curves. 



32 



fyteeMXWld ^foMAMMXf, 



Too few draughtsmen and designers possess the ability to produce 
quick freehand technical sketches, yet it offers a good many advantages 
and presents wide scope for quick and clear expression. 

A designer frequently wishes he could have before him a sectioned, 
part-sectioned or even transparent model when demonstrating, dis- 
cussing or planning some modification or improvement to an existing 
piece of mechanism. The ability to sketch with confidence and accuracy 
grows with practice so that this wish can be gratified. 

Parts can be cut away or ghosted in by the practised hand with a 
facility that almost makes a pencil into a magic wand. 

It will be found that the 30 and 60 degree angles can be estimated 
with fair accuracy and that after a little practice it will be possible to 
draw good ellipses with a single freehand sweep of the pencil. 

Many sketchers are discouraged because they have never learnt, 
or have failed to grasp, the basic rules of three-dimensional drawing, 
particularly the angles at which the ellipses are drawn on the planes 
facing left and right, yet they are confident when drawing those on the 
top plane (see Figure 26, page 24). 

How often one sees technical contributions entirely spoiled by 
the accompanying illustrations. Much of the puzzlement with regard 
to correct orientation of ellipses can be avoided if the draughtsman 
has before him a cube drawn at the aspect being used with an ellipse 
on each visible face of the cube. 

By sketching it is possible to work out a complete design down 
to the last detail so that, from then on, the orthographic general 
arrangement can be set down with great overall saving of time. 

33 



As the student progresses through the pages of this book he may 
become aware of a certain amount of repetition and of the fact that 
many of the problems can be solved in more than one way. This is done 
to foster a fuller understanding of the subject as a whole. 

The very fact that alternative methods are possible shows that the 
answers are exact geometrical solutions of a given problem and not 
convenient compromises. 

In practice the draughtsman will naturally use the method most 
suited to the particular task in hand. 



On page 40 a specially devised object is shown in orthographic views 
followed by its three-dimensional translations. It is not a drawing of 
any particular component but has been designed solely for use as an 

exercise. 

Effort has been made to embody difficult features which might 
daunt the draughtsman as yet unversed in pictorial drawing. 

Three-dimensional translations of this exercise-piece will be built 
up stage by stage, with page numbers given so that the reader may 
refer to the geometry embodied in that particular stage. 



34 



fytee<keMX& Bk&tcJlAMXf, 




Figure 4 2 




• ><* 




The drawing of complicated shapes 
from a dimensional point of view, 
such as a complete car, is not norm- 
Ta+lx dealt with in isometric drawing. 
k* There are times, however, when 
,<a^e*iigqer V»shes to visualize a sub- 
ject the^ifrmensions of which are 
^attfef in/definite because of its many 
curves./ VL/ 

U§ing- isometric as a basis, it is 
n©t difficult to build up the guide 
lines by the *so far along — so far up — 
so far in* method. Even if the product 
is not a work of art, the designer 
has at least got something down on 
paper for his own critical analysis, and so produces a basis for con- 
tinued study and experiment. 



35 



Ofcwieisue View, o^ (look&i Qea/i 




36 




EXPLODED VIEW OF 
AIR COMPRESSOR 

Figure 44 



37 



QdkoKyuzpUic. View* o/ Ga^ilWf 




FT 



7T\ 



1 






1 ii_ 

I 



ii ii 

L ii a 



■ r 



21 



c 



I 



Valve box castinq 
with cored passages. 

Figure 4 5 





Section A A 



Section CC 



38 



OiXMM&blic View- Qjj QoiilHXj, 



Fiqure 4 6 




When designing a casting which has intricate passages, a designer 
derives much benefit by using isometric, freehand or otherwise. 

By reversing conditions, showing cored passages as positive 
shapes, he helps the patternmaker to plan the moulding method with 
a great saving of time. 




Fiqure 4 7 



(Positive) Isometric view of cored passages 



39 



ORTHOGRAPHIC VIEWS 
OF EXERCISE PIECE 





Front view 



End view 




Figure 4 8 



Dimensions have been omitted 
for clarity. 



Plan 



40 




Draw Datum centre lines 
which should be marked 
to ensure clear identifica- 
tion. Convert lengths 
taken from orthographic 
views, see Figure 51 be- 
low, to isometric lengths 
and set them out on the 
Datum lines. Draw in iso- 
metric base shape, using 
light pencil lines. 




Draw thickness of flange 
above base, isometric 
scale. 



Figure 5 



See also Figures 8 and 9 



41 




The main body shape is 
now drawn in. The important 
positions marked thus: are 
found by measurements up- 
ward from the base plane and 
across, parallel with the base 
lines on the orthographic view, 
and converted to isometric 
measurements. 

It is essential that the new 
measurements are only used 
vertically or on the lines drawn 
with the 30° set square. 

Having set out the frontal 
shape, the back can be pro- 
jected as shown. The angular 
lines which form the axes of 
the circular portions are also 
determined by measurements 
converted in the usual way. 

Choose definite points on 
the orthographic view and re- 
peat them after scale conver- 
sion on the isometric view. 

In this case the topmost 
point on the axial (£ of each 
cylinder and the point where 
the cylinder axes converge on 
the vertical (£ are marked • . 

Brief Recapitulation 
Measure orthographic view 
vertically and horizontally. 
Convert to isometric scale. 
Set out in isometric directions. 



42 



Minor for I major 
/ B 



^7 



Minor for Vi 
A 




Foreshortened 

length of cyl. 

A 



In the previous stage we have established the foreshortened 
lengths of the cylinders A and B, and with this knowledge we can now 
complete what would normally be the most difficult part of the 
drawing. 

Figure 54 shows the method used for converting each of the two 
foreshortened lengths into its own particular sight angle and the geo- 
metry employed to find the ellipse proportion used for each axial <£. 

It also gives us the position of each ellipse along its axial (£. 
Reference may be made to Figure I I, page 14; Figure 15, page 17 and 
Figure 29, page 25 as these have a bearing on the particular problems 
embodied in this exercise. 



43 



NOTES 



ISOMETRIC AND TRIMETRIC DRAWING 



The value of isometric drawing as a means of illustrating such things as instructional 
handbooks has long been recognized, and greater use is now being made of it in workshop 
drawings, either to supplement, or occasionally as a substitute for, the more conventional 
orthographic views. However, as the author shows in this book, the usefulness of isometric 
and trimetric drawing does not end here. It can be a most valuable tool for the designer 

himself. 

Many otherwise experienced draughtsmen have in the past been deterred from trying 
their hands at this form of drawing by a mistaken belief that there is something mysterious 
or complicated about it; a belief which has been perpetuated by the lack of any simple and 
practical work dealing with the subject. The present -book sets out to remedy this deficiency, 
and shows that isometric and trimetric drawing are geometrically pure forms of drawing, 
well within the scope of the average draughtsman, using only standard drawing office 
techniques. 

The treatment is essentially practical; theory and basic principles are introduced as 
needed, and being linked to the immediate problem of producing a drawing, are quickly 
and easily grasped, even by the novice. After explaining the basis of isometric projection, 
the author goes on to discuss the isometric scale and its construction. The important 
subject of drawing ellipses rapidly and accurately is next dealt with, and the knowledge 
already gained is then applied to the drawing of angular subjects and attitudes. This leads 
naturally to the consideration of the isometric aspects, through which the student is 
introduced to trimetric projection. More advanced work with the ellipse follows, and the 
problems of drawing some specific subjects are then considered — helical springs, hexagon 
nuts, and irregular shapes are all dealt with in detail. Freehand drawing and sketching form 
the subjects of the next sections, and here it is shown how three-dimensional drawing can 
aid the designer in his work. Finally, following some examples of actual isometric drawings, 
a carefully designed exercise piece is presented, and the problems of drawing it are 
discussed in detail. 

The work is copiously illustrated, preference being given at all times to clear drawings 
rather than wordy explanations of the points under discussion. A large page size has been 
chosen, so that the illustrations can be reproduced in full scale. Many valuable hints and 
tips, the fruit of the author's own experience, are given, and this information, most of 
which has never previously been published, makes the book of value alike to the experienced 
draughtsman and to the student. 

PRICE |0/- NET 

A HEYWOOD BOOK 

Published by Temple Press Books Ltd 
42 RUSSELL SQUARE, LONDON WCI